Apparatus for stabilizing turbine-generator shaft torsional oscillations

ABSTRACT

An apparatus for stabilizing turbine generator shaft torsional oscillations including: a current detector for detecting ac current of a turbine generator used in combination with a dc power-transmission system, a filter to which an output of said current detector is delivered, the filter comprising a first bandpass filter for detecting a sub synchronous component (f l  -f m ) and a second bandpass filter for detecting a super synchronous component (f l  +f m ) where a fundamental freuency of the generator is represented by f l  and a natural frequency of the mechanical shaft system of the generator is represented by f m , a calculation circuit for applying conversion of at least one of d and q axis to respective outputs from the first and second bandpass filters using a generator phase θ G  to take out at least one of Δi d  and Δi q  of the sub and super synchronous components, a third bandpass filter to which an output from the calculation circuit is fed, the third bandpass filter for taking out a stabilization signal therefrom, and a circuit for controlling a converter for delivering an output of the generator to the dc power-transmission system on the basis of the stabilization signal.

BACKGROUND OF THE INVENTION

The present invention relates to a stabilization apparatus in regard tointeraction problems between turbine-generator shaft torsionaloscillations and the dc transmission control system.

Dumping D_(m) of the mechanical system of turbine-generators physicallytakes a positive value (D_(m) <0) although its value is small and isessentially stable. In the case of transmitting electric energy by thedc transmission, dumping D_(e) of the electric system when viewed fromthe generator takes a negative value (D_(e) <0) by the influence of theconstant current control considered as the fundamental control for thedc transmission in a low frequency range of 10 to 20 Hz ("HVDC-Turbinegenerator torsional interactions, A new design consideration" by M. P.Bahrman, E. V. Larsen et al. CIGRE SC14-04, 1980).

In the case where there exist some of natural frequencies of themechanical shaft system of the turbine generator, which are included insuch a low frequency range, when dc power becomes large, the resultantdumping (D_(m) +D_(e)) of the generator takes a negative value to becomeunstable. Thus, shaft torsional oscillations occur. For this problem, astabilization scheme based on the dc control system is proposed.

Sub-synchronizing dumping control (which will be referred to as "SSDC"hereinafter) is effective for stabilization over an entire range of theshaft torsional frequency. When the turbine generator is expressed asN-mass model, there exist (N-1) natural frequencies. A circuit tocollectively stabilize such oscillations is designed to apply the outputof the stabilizing circuit to the output side of the current controlregulator (which will be referred to as "ACR" hereinafter).

There are four problems to be considered in connection with interactionsbetween turbine generator shaft torsional oscillations and the dcpower-transmission system.

(1) It is considered that it is not simple to design a control systemsuch that two closed loops for essential ACR and SSDC do not interferewith each other. For SSDC, an additional closed loop control issupplemented and its output is added to the output of ACR. Accordingly,it is considered that control design harmonized with the basic controlis required for individual systems in order to obtain positive dumping(D_(e) >0) in the shaft torsional frequency range without damaging highresponse of the essential ACR.

(2) The know-how in regard to the detailed design of SSDC is socomplicated that nobody understands other than developers. Such adetailed design includes a design to set dumping values over the entirerange of the shaft torsional frequency to calculate frequencycharacteristic of SSDC for satisfying the set values to obtain highorder transfer function to approximate to this, a design to obtain atransfer function of a feedback circuit for obtaining frequencycharacteristic of a desired open loop transfer function. Thus, thedetailed design is complicated.

(3) The design of SSDC is dependent upon rather simple model in regardto the ac/dc system including the conventional basic control.Particularly in the case of the generator, since a simple voltage modelon which only the angular velocity change Δω is taken into account isused, a simulator study or field verification is assumed to be requiredfor the stabilization scheme based thereon, when applied to the actualsystem.

(4) The stabilization signal is obtained by deriving an internal voltageof the generator from the ac bus voltage by the compensation of thegenerator current in order to obtain a stabilization signal close to Δωof the generator as far as possible to input the internal voltage thusobtained to a frequency detector. However, it cannot be said thateverything possible is done concerning the study as to whether or notany other signal can be used for the stabilization signal.

SUMMARY OF THE INVENTION

With the above study on the items (1) to (4) in view, an object of thepresent invention is to provide a stabilization apparatus which permitsinteractions between the control system of the dc transmission and theturbine generator shaft torsional oscillations to be reduced withoutdamaging high response intrinsic to the dc transmission and hence isrelatively easy to design.

To achieve this object, the present invention is implemented as follows.It is first assumed that the fundamental frequency of the turbinegenerator and the natural frequencies involved in mechanical shaftsthereof are represented by f₁ and f_(m), respectively. Subsynchronouscomponent (f₁ -f_(m)) and super synchronous component (f₁ +f_(m)) aredetected using bandpass filters, respectively. These components thusdetected are subjected to the conversion on at least one of d and q axisusing a generator phase θ_(G). Thus, at least one of Δi_(d) and Δi_(q)of the sub-synchronous component and the super synchronous component istaken out. By passing the component thus taken out through a bandpassfilter, a stabilization signal is taken out. The stabilization signalthus obtained is used for control of converters in the dc transmission.

Namely, this stabilization signal is formed on the basis of thefollowing parameters.

[1] d, q axis conversion variables Δi_(d) and Δi_(q) of the sub andsuper synchronous components which are sideband waves of the fundamentalfrequency current.

[2] Synchronous phase error Δθ_(ep) of a phase lock loop (which will bereferred to as "PLL" hereinafter) of the synchronizing circuit.

The verification of the stabilization effect by the stabilization signalis based on the instantaneous value calculation of the ac/dc systemincluding commutation of thyristors using EMTP (Electro MagneticTransients Program developed by the Bonneville Power Administration inU.S.A.). The generator model of EMTP is developed for analysis of shafttorsional oscillations of this kind. N-masses model including respectivestages of the turbine, e.g., high, medium and low pressure turbines andthe generators as mass points is assumed. The control system therefor,particularly PLL for phase control simulates the system equivalent tothe actual one. Accordingly, the verification is possible in a mannerclose to the actual system.

For the time being, there is no simulator for the turbine generator,which is capable of simulating multimass point comparable to the actualsystem. Accordingly, it is regarded as the best that the verification ofthe analysis of the shaft torsional oscillations is based on the EMTPsimulation.

The stabilization mechanism of the shaft torsional oscillations using aphasor diagram and the action of the stabilization signal will be nowdescribed.

Consideration is taken in connection with changes due to the shafttorsional oscillations as the electric torque T_(e) and the generatorrotor speed ω under condition where the mechanical shaft torsionalsystem is opened in the ac/dc closed loop.

    ΔT.sub.e /Δω=D.sub.e +jK.sub.e           ( 1)

For consideration of changes expressed as phasors ΔT_(e) and Δω, thereal part of the right side of the equation (1) is defined as theelectric dumping D_(e) (p.u.). The outline of the D_(e) calculationmethod having been developed is as follows.

Each valve commutation is calculated in terms of the three phaseinstantaneous value to separate the valve current into sub and supersynchronous components which are sideband waves of the fundamentalfrequency by the Fourier analysis. The sub and super synchronouscomponents thus obtained are subjected to d, q axis conversion tointerface with the generator. The generators are modeled by Park'sequation. The convergence of Δω and other changes is obtained by theiteration. Thus, D_(e) is obtained as the real part of the phasor ΔT_(e)/Δω.

Since the dc control system essentially consists of the constant currentcontrol and ac component Δi_(dc) is superimposed on dc current due tothe shaft torsional oscillation, the control angle α changes byvariation Δα. The Δα is composed of two components as described below.

    Δα=Δα.sub.R +Δθ.sub.ep ( 2)

These components are a Δα_(R) (electric angle) related to the regulatoroutput Δe_(R) (volt) by the feedback of Δi_(dc) and a synchronous phaseerror Δθ_(ep), respectively.

The synchronizing circuit has an AC bus voltage as its input and issynchronized by PLL. AC bus voltage phase Δθ_(AC) due to the shafttorsional vibration is calculated from the generator phase Δθ_(G). Thephase relationship therebetween is shown in FIG. 2.

An angle with respect to the q axis of the generator is referred to asδ_(AC) as the AC bus voltage V_(AC) =ed+je_(q). From the phasor diagramin FIG. 2, the following relationships are obtained.

    θ.sub.AC -θ.sub.G =π/2-δ.sub.AC

    tan δ.sub.AC =e.sub.d /e.sub.q

When the above equation is linealized, the following relationships areobtained. ##EQU1## Since Δe_(d) and Δe_(q) have been calculated in thecalculation of D_(e), Δθ_(AC) can be calculated from the above equation.

If the frequency bandwidth of the closed loop of PLL is approximately 5Hz, the synchronous output Δθ_(op) for the shaft torsional oscillationof 10 to 20 Hz is delayed with respect to Δθ_(AC), resulting inoccurrence of the synchronous phase error Δθ_(ep). The relationshiptherebetween is shown in the following equation (3).

    Δθ.sub.AC -Δθ.sub.op =Δθ.sub.ep ( 3)

When the transfer function of the closed loop of PLL is expressed in aquadratic form, Δθ_(ep) is expressed as follows: ##EQU2##

Further, when the characteristic parameter of PLL is given, phasorΔθ_(ep) (jω_(m)) is calculated as S=jω_(m) and ω_(m) =2πf_(m) forsinusoidal wave excitation due to the shaft torsional oscillations.

FIG. 3 illustrates the relationships expressed as the above-mentionedequations (2) and (4) on the output side of the regulator wherein barsattached to symbols indicative of changes denote vectors. In addition,Δe_(syn) is obtained by applying voltage conversion to Δθ_(ep)(rad/electric angle).

If the stabilization signal Δe_(st) is not considered, the relationshipexpressed as the following equation (5) holds, which corresponds to theequation (2).

    Δe.sub.c2 =Δe.sub.R +Δe.sub.syn          ( 5)

In this equation, Δe_(c2) corresponds to Δα and Δα denotes a net changeof the control angle with respect to zero point of the actualcommutation voltage. Accordingly, Δe_(c2) can be regarded as aneffective change of the phase control signal e_(c).

As well known, the dc voltage decreases as the control angle increases.Accordingly, since there exists a relationship such that when Δα>0,ΔV_(dc) <0, whereas when Δα<0, ΔV_(dc) >0, there is a tendency to have arelationship such that Δe_(c2) and ΔV_(dc) are opposite to each other inphase. The ac component ΔV_(dc) of the dc voltage produces Δi_(dc)through the dc transmission impedance Z_(dc) (jω).

    Δi.sub.dc =ΔV.sub.dc /Z.sub.dc (jω)      (6)

Assuming now that Δi_(dc) is produced from Δe_(c2), the correspondingnumerical gain, i.e., Δi_(dc) /Δe_(c2) does not so much change withrespect to individual shaft torsional frequency. Further, since thephase difference between Δi_(dc) and ΔT_(e) is relativley small in theisolated dc transmission according to the calculated result, it isconsidered that the phase difference between Δe_(c2) and ΔT_(e) does notso much change.

On the basis of the qualitative tendency of the above-mentioned variousphasors, the stabilization mechanism of the shaft torsional oscillationswill be now considered. The tendency of various phasors obtained by theD_(e) calculation is shown in FIG. 4(a). This represents therelationship of the equation (5) showing the example where thestabilization signal is off and D_(e) <0.

(1) An angle θ_(s) that ΔT_(e) and Δ107 form is greater than 90 degrees,which corresponds to D_(e) <0.

(2) An angle that Δω and Δθ_(G) form is π/2 (rad.).

(3) An angle θ_(syn) that Δθ_(G) and θe_(syn) form is equal to ∠F_(p)(jω_(m)) (cf. equation (4)).

By introducing the stabilization signal Δe_(st), stabilization will benow considered (FIG. 4(b)). A resultant signal Δe_(c1) of the regulatoroutput Δe_(R) and the stabilization signal Δe_(st) is obtained (FIG. 3).

    Δe.sub.c1 =Δe.sub.R -Δe.sub.st           ( 7)

In this case, if Δe_(R) of ACR is delayed by -Δe_(st), Δe_(c2) lags.Assuming that the phase of Δω is constant, the phase of Δe_(syn) alsodoes not change and the delay of Δe_(c2) delays Δi_(dc) and ΔT_(e).Thus, when ΔT_(e) lags Δω by a phase angle more than 270 degrees, thephase difference is expressed as θ_(s) <90 degrees (D_(e) >0).

For the stabilization signal, a signal which slightly leads an invertedsignal of Δe_(R) is suitable. It is required to constitute such a signalwith signals directly available at the converter station. Astabilization signal is chiefly formed by the above-described two kindsof signals. By introducing the stabilization signal thus obtained as anaxiliary signal using the D_(e) calculation method, stabilization isconfirmed.

BRIEF DESCRIPTION OF THE DRAWINGS

In the drawings:

FIG. 1 is a block diagram illustrating the configuration of anembodiment according to the present invention;

FIG. 2 is a block diagram illustrating the configuration of PLL used ina synchronizing circuit;

FIG. 3 is a block diagram illustrating the configuration of a circuitwhich deals variation Δα of the control angle and the synchronous phaseerror Δθ_(ep) ;

FIG. 4(a) is a phasor diagram showing calculated examples of variousphasors in D_(e) calculation in connection with the current control loopshown in FIG. 3;

FIG. 4(b) is a phasor diagram showing the stabilization mechanism;

FIG. 5(a) is a phasor diagram showing the phase relationship betweenphasors derived from sub/super synchronous components and control signalhaving been calculated in the case of f_(m) =8.33 Hz;

FIG. 5(b) is an explanatory view showing a method of formingstabilization phasors by the super synchronous component;

FIGS. 6(a) and 6(b) show the shaft torques with and without thestabilization signal respectively to indicate the effect of the presentinvention on the shaft torsional oscillation.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

The present invention will be described in detail in connection with apreferred embodiment with reference to attached drawings.

FIG. 1 shows, in a block form, an example of the configuration of anapparatus according to the present invention. In this example, thegenerator is assumed to be the five-mass model, viz., the modelcomprising high, medium and two low pressure turbines, and the generatoritself. In the example of this model, there appear four shaft torsionalfrequencies (f_(m)) of 8.33, 16.6, 21.5 and 22.5 Hz. In the followingdiscussion, these frequencies will be handled with their beingclassified into three groups, i.e., about 10 Hz, 10 to 20 Hz and morethan 20 Hz.

Initially, in the case that the shaft torsional frequency f_(m) isapproximately 10 Hz, a signal derived from the super synchronouscomponent is used as the stabilization signal. Three phase currentsi_(a), i_(b) and i_(c) on the primary side of a converter transformer 4are employed as an input of the apparatus. By passing these three phasecurrents through a bandpass filter (which will be referred to as "BPF"hereinafter) 15 of the resonant frequency (f₁ +f_(m)), super synchronouscomponents Δi_(a), Δi_(b) and Δi_(c) are obtained wherein f₁ denotes afundamental frequency. For applying d, q axis conversion to these threephase variables, sin and cos of the phase angle θ_(G) of the generatoris multiplied. Thus, Δi_(q-sp) and Δi_(d-sp) are obtained from the supersynchronous component. It is to be noted that multiplication of cos canbe omitted as described later. ##EQU3##

For obtaining θ_(G), application of a phase output θ_(op) of a PLL 13 ofthe synchronizing circuit is considered. Since there is a phasedifference Φ_(p) therebetween in general, this phasse difference istaken into account.

    θ.sub.G =θ.sub.op +Φ.sub.p

By inputting θ_(G) to a function generator 14, sin function isgenerated. The sin function thus obtained is multiplied by thepreviously described Δi_(a), Δi_(b) and Δi_(c) at a multiplier 16. Bysumming outputs from the multiplier 16, -Δi_(q-sp) corresponding to theequation (8) is obtained. By passing -Δi_(q-sp) through a BPF 20a of theresonant frequency f_(m), a stabilization signal Δe_(st) is prepared.The stabilization signal Δe_(st) thus obtained is subjected to summingoperation on the output side of the constant current control regulator11.

In regard to Q factor of BPF, as an example, Q factors of the input andoutput BPFs 15 and 20 are 5 and 1, respectively.

In the case of 10 Hz<f_(m) <20 Hz, a synchronous phase error Δθ_(ep) ofthe PLL 13 is used as the stabilization signal. This Δθ_(ep) issubjected to subtracting operation on the output side of the regulator11 through a phase-leading circuit 21 and the BPF 20b of the resonantfrequency f_(m).

In the case of f_(m) ≧20 Hz, a quantity of -Δi_(q-sp) derived from thesub synchronous component is used as the stabilization signal. In thiscase, the previously described super synchronous component is solelyreplaced with the sub synchronous component, but the configuration isjust the same as the previous case. The configuration in this caseincludes an input BPF 17 of a resonant frequency (f₁ -f_(m)), amultiplier 18, an adder 19b, and an output BPF 20c of the resonantfrequency f_(m). It is to be noted that the polarity of the adder 12 isminus.

In this embodiment, the practically unacceptable frequency range of theshaft torsional oscillation mode frequency is assumed to be 8 to 25 Hz.As a result of the EMTP calculation, it has been seen that it issuitable for attainment of attenuation effect over the entire mode todivide the above-mentioned frequency range into high, medium and lowfrequency ranges to apply the stabilization signal thereto.

In the application of the stabilization signal, care must be taken inthe following problems.

(1) Commonly using the stabilization signal in two modes is notpreferable because respective attenuation effects are reduced. This isdue to the fact that the gain of the stabilization signal for each modeis required to be reduced to one half in view of suppression of higherharmonic ripples.

(2) Since the stabilization effect of the sub/super synchronouscomponent has strong frequency dependency, suitable selection isrequired.

(3) There is an interference between modes of the stabilization signal.Particularly, when frequencies in the medium and high modes arerelatively close to each other, there is a tendency that sucn aninterference occurs.

The stabilization is confirmed on the basis of the D_(e) calculation inconnection with respective stabilization signals and the detailedexplanation will be made as follows.

(1) Synchronous phase error Δθ_(ep) (Δe_(syn))

There is a tendency that according as this signal is stabilized, anangle that this signal and the regulator output Δe_(R) form becomessmall. By inverting the polarity, a vector to cancel Δe_(R) is obtained.Thus, Δθ_(ep) is easily taken out. Since PLL has the AC bus voltage assynchronous input, this value is assumed to be delayed a little ascompared to Δθ_(ep) calculated from Δω of the generator. Thephase-leading circuit 21 corrects this delay. The D_(e) calculationincluding this stabilization signal is performed. Thus, thesynchronizing phase error Δθ_(ep) (Δe_(syn)) is stabilized. The resultof D_(e) >0 is obtained.

(2) Super/sub synchronous component

When the fundamental frequency and the shaft torsional frequency arerepresented by f₁ and f_(m), respectively, there occur in the generatorcurrent, a so called sub synchronous component having a frequency (f₁-f_(m)) and a super synchronous component having a frequency (f₁ +f_(m))in addition to the fundamental wave having the frequency f₁. Since thesecurrent components are naturally included in the converter current inthe isolated dc-transmission, they are calculated by Fourier analysis.Thus, such components are intended to be used as the stabilizationsignal.

For shortening one time period of the Fourier analysis, f_(m) isselected so that f₁ /f_(m) makes a suitable ratio of integer. Forexample, in the system where the fundamental wave has a frequency f₁ of50 Hz, it is sufficient that four cycles of the fundamental wave formone time period of the Fourier analysis when f_(m) =12.5 Hz. From theanalysis of the three phase current of the converter, (f₁ ±f_(m)) can beregarded as positive sequence components, respectively. In addition,since (f₁ ±f_(m)) components can be regarded as changes with respect tothe fundamental f₁ component, they are subjected to d, q axisconversion, whereby Δi_(d) and Δi_(q) are obtained. In accordance withthe conversion formula from well known three phase currents i_(a), i_(b)and i_(c) to i_(d) and i_(q), the conversion formula is performed bymultiplying sin and cos of the phase angle θ_(G) of the generator by theabove three phase currents. When changes of i_(d) and i_(q) aresubjected to linearization, the following relational equations (10) and(11) are obtained. ##EQU4##

It is to be noted that when three phase currents are represented byi_(ao) +Δi_(a), i_(bo) +Δi_(b) and i_(co) +Δi_(c), the steady statecurrent of phase a and its change are expressed as follows: ##EQU5##

Both steady state currents of phases b and c and their changes areshifted by 2π/3 and 4π/3 with respect to the equation (1), respectively.

There are relationships related to the phase of the generator as shownbelow.

    θ.sub.G =θ.sub.GO +Δθ.sub.G, θ.sub.GO =ω.sub.1 t-Φ.sub.G,

    ω.sub.sb =2π(f.sub.1 -f.sub.m),

    ω.sub.sp =2π(f.sub.1 -f.sub.m)

As seen from the equations (10) and (11), Δi_(d) and Δi_(q) consist ofthree components, respectively. By phasor representation, there can becompared with the above-described phasors related to the stabilizationmechanism.

Equations (10) and (11) are represented by phasor.

    ΔI.sub.d =ΔI.sub.d-sb +ΔI.sub.d-sp +K.sub.1 Δθ.sub.G

    ΔI.sub.q =ΔI.sub.q-sb +ΔI.sub.q-sp +K.sub.2 Δθ.sub.G                                      (13)

It is to be noted that instantaneous values (t representation) areassumed to be equal to the imaginary part of phasor. An example ofcalculation is shown in FIG. 5(a) wherein phasors having been explainedin relation to the stabilization mechanism and phasors derived fromsub/super synchronous components are shown on the left and right sides,respectively. In the D_(e) calculation, the stabilization phasor of thesuper synchronous component with respect to the lower frequency mode isgiven as follows.

    Δe.sub.st =(ΔI.sub.d-sp +ΔI.sub.q-sp)*K, K>0 (14)

This phasor is added to the regulator output Δe_(R) as -Δe_(st)(equation (7)).

The stabilized D_(e) calculation result is shown in FIG. 5(b).-ΔI_(q-sp) which is the phasor representation of -Δi_(q-sp) correspondsto the equation (14). It is to be noted that the phase of the phasorequivalent to the equation (14) is obtained by leading the phase ofΔI_(q-sp) by π/4 without using ΔI_(d-sp).

In the sin function generator 14 in FIG. 1, when θ_(G) is substitued for(θ_(G) -π/4), the phasor ΔI_(q-sp) lead by a phase angle of +π/4.

Accordingly, it is sufficient that the phase difference Φ_(p) foradjustment for obtaining θ_(G) of the generator from θ_(op) of PLL issubstituted for Φ_(p) -π/4. Thus, the calculation of ΔI_(d-sp) becomesunnecessary. As a result, the calculation of the cos functioncorresponding to the sin function can be omitted.

The adjustment phase Φ_(p) permits the phase adjustment of thestabilization phasor, but is basically a fixed angle. For example, forEMTP, Φ_(p) is a constant as defined below.

Since the synchronous phase output θ_(op) is coincident with the inputphase θ in a steady state when the ac bus voltage of the converter isassumed to be a synchronous input of PLL, the ac bus voltage e_(a) isexpressed as follows.

    e.sub.a =E.sub.a cos θ=E.sub.a cos θ.sub.op    (15)

On the other hand, when the phase angle of the generator is representedby θ_(G), the ac bus voltage e_(a) is expressed, in accordance withEMTP, as follows. ##EQU6##

By allowing the equations (15) and (16) to correspond to each other,Φ_(p) is calculated as follows.

From θ_(G) -π/2-δ_(s) =θ_(op), Φ_(p) =π/2+δ_(s) is obtained.

In FIG. 1, the quantity -Δi_(q-sb) derived from the sub synchronouscomponent is taken as the stabilization signal over the higher frequencymode. The reason why its polarity in the adder 12 is taken in a manneropposite to that of the super synchronous component is that ΔI_(q-sb)has substantially antiphase relationship with respect to ΔI_(q-sp) inprinciple, (FIGS. 5(a) and 5(b). FIGS. 5(a) and 5(b) show an example ofcalculation of lower frequency mode. Such a tendency does not change forhigher frequency mode.

The reason why a quantity derived from the super synchronous componentis used for the lower frequency mode and a quantity derived from the subsynchronous component is used for the higher frequency mode is asfollows.

By rewriting Δθ_(G) /Δθ_(G) for instantaneous value/phasor with ε/ε,these parameters are defined as follows.

    Δθ.sub.G =ε=ε sin ω.sub.m t

    Δθ.sub.G =ε=ε.sub.e jω.sub.m t (18)

where ω_(m) =2πf_(m) and f_(m) is shaft torsional frequency.

Then, by applying the phasor relationship expressed as Δθ_(G) =ε to theabove-mentioned equation (13), phasors I_(d)ε and I_(q)ε are defined.

    ΔI.sub.d /ε=I.sub.dε-sb +I.sub.dε-sp +K.sub.1 =I.sub.dε

    ΔI.sub.q /ε=I.sub.qε-sb +I.sub.qε-sp +K.sub.2 =I.sub.qε                                         (19)

I_(d)ε and I_(q)ε are obtained by dividing respective terms of the rightside of the equation obtained with individual D_(e) calculation by ε.D_(e) is calculated as the real part of ΔT_(e) /Δω as follows. As wellknown, ΔT_(e) is first expressed as follows. ##EQU7##

Assuming that the AVR effect of the third term of the right side isnegligible, when p=jω_(m) (pu), the phasor representation of theequation (20) is as follows.

    ΔTe=[E.sub.fd -(x.sub.d -x.sub.q (jω.sub.m))i.sub.do ]ΔI.sub.q +(x.sub.q -x.sub.d (jω.sub.m))i.sub.qo ·ΔI.sub.d                                  (21)

Further, ΔI_(q) and ΔI_(d) are replaced with ε·I_(q)ε and ε·I_(d)ε usingthe equation (19), respectively. The phasor Δω is expressed as follows.##EQU8##

Dividing equation (21) by equation (22) to obtain the real part D_(e),D_(e) is expressed as follows. ##EQU9## where * represents conjugatephasor, and A, B, C and D represent positive constants obtained from thegenerator constant and have the relationship expressed as A>>B, C>>D.

Accordingly, when phasors which respectively lag the phasors I_(d)ε andI_(q)ε by 90 degrees are prepared, D_(e) is substantially proportionalto the real parts thereof.

The contribution to D_(e) of the super/sub synchronous components isobtained as follows.

The super/sub synchronous component is composed of the following twocomponents. These components are expressed using phasors I_(d)ε andI_(q)ε as follows:

(a) The contribution based on a change ΔI=Δi_(d) +jΔI_(q) of thegenerator current.

    sub component=-(I.sub.qε *-jI.sub.dε *)ε/2

    super component=(I.sub.qε -jI.sub.dε)ε/2 (24)

(b) The contribution based on a change of the phase of the steady statevalue I_(o) =i_(do) +jI_(qo) of the generator current.

    sub component=-(i.sub.do +ji.sub.qo)ε/2

    super component=(i.sub.do +ji.sub.qo)ε/2           (25)

The sum of the above-mentioned (a) and (b) gives the sub/supersynchronous components.

When the above four vectors are resolved in directions of the phasorsI_(d)ε and I_(q)ε, respectively, the contribution to D_(e) can be seenfrom the equation (23). The above four phasors have been calculated inconnection with respective stable/unstable examples of the shafttorsional oscillations of three frequencies of 8.33, 16.67 and 20.0 Hz,and the phasors contributing to D_(e) >0 have been studied. As a result,it has been that the following two frequencies have such a tendency.

(a) super synchronous component of the low frequency (8.33 Hz).

(b) sub synchronous component of high frequency (20 Hz).

Others have a small effect with respect to D_(e) (D_(e) ≈0) or adverselycontribute to D_(e) <0.

The reason why the super/sub synchronous components of the above (a) and(b) are used has been stated above.

ADVANTAGES WITH THE EMBODIMENT

The advantages with the present invention are demonstrated by digitalsimulation based on EMTP. When shaft torsional oscillations are exciteddue to a rapid deblock of 100% of the dc transmission system, thecomparison between off and on of the stabilization signal in connectionwith the shaft torque T₄ between a generator and the adjacent turbinewhich is not shown is shown in FIGS. 6(a) and (b). In this example, thestabilization signals of FIG. 1 are used.

In the D_(e) calculation, the effects with the single stabilizationsignal are calculated in connection with the corresponding shafttorsional frequency. Further, the mechanical torsional system is openedto calculate D_(e) in the open loop. On the other hand, the actualsystem has four shaft torsional mode frequencies in this example. Sincethree stabilization signals are applied thereto, it is necessary toverify that attenuation effect in the closed loop including themechanical system in the same manner as in the actual system. The wholeattenuation tendency can be seen from FIG. 6 when the stabilizationsignals are on, but attenuation of each mode cannot be seen.Accordingly, Fourier analysis of the waveforms are conducted to comparethem. An example of this calculation is shown in Table 1.

                  TABLE 1                                                         ______________________________________                                        The effects of stabilization signals                                          Time                                                                          OFF             ON                                                            mode  1       2      3    1     2    3    Note                                ______________________________________                                        1     10.5%   6.3    9.0  7.5%  4.5  3.0  time in                                                                       seconds                                                                       OFF:                                                                          FIG. 6(a)                           2     27.5    26.0   24.0 21.0  14.5 7.0                                      3     4.0     2.5    5.0  4.5   1.0  2.5  ON:                                                                           FIG. 6(b)                           4     8.1     6.5    3.0  8.3   6.5  4.0                                      ______________________________________                                    

Table 1 shows a transient attenuation of a shaft torsional oscillationhaving a large amplitude at the earlier stage of disturbance when thestabilization signal is off. It is assumed that shaft torsionaloscillations of the first and second modes last thereafter, i.e., do notnaturally attenuate. The reason is that the D_(e) calculation resultsrelated thereto show D_(e) ≦-2.0 pu at the dc loading of 100%,respectively.

On the other hand, there is a tendency that all the modes attenuate inthe application of three kinds of stabilization signals in FIG. 1. Whenthe stabilization signals of the first and second modes are on and thestabilization signals of higher modes (the third and fourth modes) areoff, shaft torsional oscillations of the first and second modes exhibitbetter attenuation effect rather than in Table 1. In contrast, shafttorsional oscillations of higher modes have poor attenuation effect andturn to lasting or increasing tendency. When stabilization signals ofall modes are off, there appears natural attenuation tendency for highermodes (Table 1). This is assumed to result from the fact that thecharacteristic of D_(e) essentially shows D_(e) >0 in higher frequencyrange. This is also assumed to originate from the fact that whenstabilization signals of the first and second modes are applied, highermodes are caused to exhibit D_(e) <0 as a reaction thereof.

Accordingly, stabilization signals are required even for higher modes inorder to obtain the attenuation tendency over the entire mode, resultingin the necessity of the configuration in FIG. 1.

OTHER EMBODIMENT

Since there is a tendency that the stabilization signal of the highermode interferes with the stability effect of the second mode, an on/offcontrol of the higher frequency signal is assumed to be conducted.First, in the case of failure of the ac/dc system, when a shafttorsional oscillation is excited to much extent, the stabilizationsignal of the higher frequency mode is turned off for about 3 sec. Atthis time period, effective attenuation of the first and second modes isobtained by two stabilization signals of the first and second modes. Forfurther enhancing the attenuation effect, addition of a Δf signal iseffective. When Δf obtained from the ac bus voltage through a frequencysensor is used together with stabilization signals of the first andsecond modes, it is realized by the EMTP simulation that thestabilization signals of the first and second modes attenuate below 2%in about 3 sec. In contrast, when only Δf is used, the attenuationeffect of the first and second modes can be hardly anticipated. In thisinstance, Δf is added in consideration of the polarity on the outputside of the regulator without using BPF, etc.

On the other hand, the higher mode occupies the greater part of residualripples of the shaft torsional oscillation by the stabilization signalplaced in off state after 3 sec. have passed. At this stage, by makinguse of the stabilization signal of the higher mode, the higher mode iscaused to attenuate. For the first and second modes, they attenuatebelow about 2% for the first 3 sec. and after the higher frequencysignal is turned on the state of D_(e) >0 is maintained over all themode frequencies.

ADVANTAGES WITH THE PRESENT INVENTION

(1) There is less interference with respect to high response of theconstant current control which is the basic control of the dctransmission. Since a stabilization signal is obtained through a filtertuned to the shaft torsional oscillation frequency of the generator toadd the stabilization signal to the output side of the regulator usingan open loop, when the shaft torsional frequency is stabilized, thestabilization signal disappears. Since a bandpass filter is provided inthe signal path, there is less interference with respect to the basiccontrol system by other frequencies.

(2) Conventional basic control system can be applied as it is. Wherethere is the problem of the shaft torsional oscillation, it is possibleto add the stabilization signal later. In general, mode frequencies ofshaft torsional oscillations are known values for individual plants andthe number of modes is not so many. Since the apparatus according to thepresent invention provides optimum stabilization signals for low, mediumand high frequency ranges of the shaft torsional oscillation frequency,it is sufficient to design these signals differently from the basiccontrol to add them. Accordingly, the countermeasure for the shafttorsional oscillation frequency can be completely independently takenwith the conventional basic control system being as it is, resulting insmall burden in control system design.

(3) Since the stabilization signal is constituted with easily availablecomponents at a convertor station, there is a little problem inpractical use. The synchronous phase of PLL is utilized as the generatorphase θ_(G) necessary for obtaining d, q axis components.

What is claimed is:
 1. An apparatus for stabilizing turbine generatorshaft torsional oscillations including:(a) a current detector fordetecting ac current of a turbine generator used in combination with adc power-transmission system; (b) a filter to which an output of saidcurrent detector is delivered, said filter comprising a first bandpassfilter for detecting a sub synchronous component (f₁ -f_(m)) and asecond bandpass filter for detecting a super synchronous component (f₁-f_(m)) where fundamental frequency of said generator is represented byf₁ and a natural frequency of the mechanical shaft system of saidgenerator is represented by f_(m) ; (c) a calculation circuit forapplying conversion of at least one of d and q axis to respectiveoutputs from said first and second bandpass filters using a generatorphase θ_(G) to take out at least one of Δi_(d) and Δi_(q) of the sub andsuper synchornous components; (d) a third bandpass filter to which anoutput from said calculation circuit is fed, said third bandpass filterfor taking out a stabilization signal therefrom, and a circuit forcontrolling a converter for delivering an output of said generator tosaid dc power-transmission system on the basis of said stabilizationsignal.
 2. An apparatus as set forth in claim 1, wherein there isprovided means for detecting said generator phase θ_(G) from asynchronizing circuit in said circuit for controlling said converter asa synchronous phase output θ_(op).
 3. An apparatus as set forth in claim2, further comprises a fourth bandpass filter for taking out saidnatural frequency f_(m) from said synchronous phase error changeΔθ_(ep), an output from said fourth bandpass filter being delivered tosaid converter.